Epoch Detection -- A Method for Resolving Overlapping Signals

Consider a signal composed of a train of overlapping wavelets.* The wavelets may, for one reason or another, arrive at the receiver (or measuring apparatus) delayed by different amounts of time. The time delays of the individual wavelets are unknown, but their differences may be relatively small so that the wavelets overlap. The beginning instant of each wavelet is called an epoch. These signals are corrupted with Gaussian noise. Our problem is to detect the overlapping in time. In other words, we wish to design a practical system which enables us to resolve the received signal train into overlapping wavelets and to describe them individually. The theory of statistical detection of signals buried in noise has been well established.1-4 In the field of resolving overlapping wavelets, Hel* We use the word "wavelets" for the individual overlapping wavelets, and reserve the word "signal" for the over-all signal train. 401 402 T H E B E L L SYSTEM T E C H N I C A L J O U R N A L , MARCH 1965